// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007 Julien Pommier
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

/* The sin and cos and functions of this file come from
 * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
 */

#ifndef EIGEN_MATH_FUNCTIONS_SSE_H
#define EIGEN_MATH_FUNCTIONS_SSE_H

namespace Eigen {

namespace internal {

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
plog<Packet4f>(const Packet4f& _x)
{
	return plog_float(_x);
}

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet2d
plog<Packet2d>(const Packet2d& _x)
{
	return plog_double(_x);
}

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
plog2<Packet4f>(const Packet4f& _x)
{
	return plog2_float(_x);
}

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet2d
plog2<Packet2d>(const Packet2d& _x)
{
	return plog2_double(_x);
}

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
plog1p<Packet4f>(const Packet4f& _x)
{
	return generic_plog1p(_x);
}

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
pexpm1<Packet4f>(const Packet4f& _x)
{
	return generic_expm1(_x);
}

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
pexp<Packet4f>(const Packet4f& _x)
{
	return pexp_float(_x);
}

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet2d
pexp<Packet2d>(const Packet2d& x)
{
	return pexp_double(x);
}

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
psin<Packet4f>(const Packet4f& _x)
{
	return psin_float(_x);
}

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
pcos<Packet4f>(const Packet4f& _x)
{
	return pcos_float(_x);
}

#if EIGEN_FAST_MATH

// Functions for sqrt.
// The EIGEN_FAST_MATH version uses the _mm_rsqrt_ps approximation and one step
// of Newton's method, at a cost of 1-2 bits of precision as opposed to the
// exact solution. It does not handle +inf, or denormalized numbers correctly.
// The main advantage of this approach is not just speed, but also the fact that
// it can be inlined and pipelined with other computations, further reducing its
// effective latency. This is similar to Quake3's fast inverse square root.
// For detail see here: http://www.beyond3d.com/content/articles/8/
template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
psqrt<Packet4f>(const Packet4f& _x)
{
	Packet4f minus_half_x = pmul(_x, pset1<Packet4f>(-0.5f));
	Packet4f denormal_mask =
		pandnot(pcmp_lt(_x, pset1<Packet4f>((std::numeric_limits<float>::min)())), pcmp_lt(_x, pzero(_x)));

	// Compute approximate reciprocal sqrt.
	Packet4f x = _mm_rsqrt_ps(_x);
	// Do a single step of Newton's iteration.
	x = pmul(x, pmadd(minus_half_x, pmul(x, x), pset1<Packet4f>(1.5f)));
	// Flush results for denormals to zero.
	return pandnot(pmul(_x, x), denormal_mask);
}

#else

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
psqrt<Packet4f>(const Packet4f& x)
{
	return _mm_sqrt_ps(x);
}

#endif

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet2d
psqrt<Packet2d>(const Packet2d& x)
{
	return _mm_sqrt_pd(x);
}

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet16b
psqrt<Packet16b>(const Packet16b& x)
{
	return x;
}

#if EIGEN_FAST_MATH

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
prsqrt<Packet4f>(const Packet4f& _x)
{
	_EIGEN_DECLARE_CONST_Packet4f(one_point_five, 1.5f);
	_EIGEN_DECLARE_CONST_Packet4f(minus_half, -0.5f);
	_EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inf, 0x7f800000u);
	_EIGEN_DECLARE_CONST_Packet4f_FROM_INT(flt_min, 0x00800000u);

	Packet4f neg_half = pmul(_x, p4f_minus_half);

	// Identity infinite, zero, negative and denormal arguments.
	Packet4f lt_min_mask = _mm_cmplt_ps(_x, p4f_flt_min);
	Packet4f inf_mask = _mm_cmpeq_ps(_x, p4f_inf);
	Packet4f not_normal_finite_mask = _mm_or_ps(lt_min_mask, inf_mask);

	// Compute an approximate result using the rsqrt intrinsic.
	Packet4f y_approx = _mm_rsqrt_ps(_x);

	// Do a single step of Newton-Raphson iteration to improve the approximation.
	// This uses the formula y_{n+1} = y_n * (1.5 - y_n * (0.5 * x) * y_n).
	// It is essential to evaluate the inner term like this because forming
	// y_n^2 may over- or underflow.
	Packet4f y_newton = pmul(y_approx, pmadd(y_approx, pmul(neg_half, y_approx), p4f_one_point_five));

	// Select the result of the Newton-Raphson step for positive normal arguments.
	// For other arguments, choose the output of the intrinsic. This will
	// return rsqrt(+inf) = 0, rsqrt(x) = NaN if x < 0, and rsqrt(x) = +inf if
	// x is zero or a positive denormalized float (equivalent to flushing positive
	// denormalized inputs to zero).
	return pselect<Packet4f>(not_normal_finite_mask, y_approx, y_newton);
}

#else

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
prsqrt<Packet4f>(const Packet4f& x)
{
	// Unfortunately we can't use the much faster mm_rsqrt_ps since it only provides an approximation.
	return _mm_div_ps(pset1<Packet4f>(1.0f), _mm_sqrt_ps(x));
}

#endif

template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet2d
prsqrt<Packet2d>(const Packet2d& x)
{
	return _mm_div_pd(pset1<Packet2d>(1.0), _mm_sqrt_pd(x));
}

// Hyperbolic Tangent function.
template<>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
ptanh<Packet4f>(const Packet4f& x)
{
	return internal::generic_fast_tanh_float(x);
}

} // end namespace internal

namespace numext {

template<>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float
sqrt(const float& x)
{
	return internal::pfirst(internal::Packet4f(_mm_sqrt_ss(_mm_set_ss(x))));
}

template<>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double
sqrt(const double& x)
{
#if EIGEN_COMP_GNUC_STRICT
	// This works around a GCC bug generating poor code for _mm_sqrt_pd
	// See https://gitlab.com/libeigen/eigen/commit/8dca9f97e38970
	return internal::pfirst(internal::Packet2d(__builtin_ia32_sqrtsd(_mm_set_sd(x))));
#else
	return internal::pfirst(internal::Packet2d(_mm_sqrt_pd(_mm_set_sd(x))));
#endif
}

} // end namespace numex

} // end namespace Eigen

#endif // EIGEN_MATH_FUNCTIONS_SSE_H
